Revisiting the Dynamics of Two-Body Problem in the Framework of the Continued Fraction Potential

In this analytical study, a novel solving method for determining the precise coordinates of a mass point in orbit around a significantly more massive primary body, operating within the confines of the restricted two-body problem (R2BP), has been introduced. Such an approach entails the utilization o...

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Bibliographic Details
Published in:Mathematics (Basel) 2024-02, Vol.12 (4), p.590
Main Authors: Ershkov, Sergey, Mohamdien, Ghada F., Idrisi, M. Javed, Abouelmagd, Elbaz I.
Format: Article
Language:English
Subjects:
Approximation
continued fraction potential
Continued fractions
dynamics of a mass point
Equations of motion
Kepler’s formulation of R2BP
Many-body problem
Mathematical analysis
Mathematical research
Mechanics
Polar coordinates
Radiation
restricted two-body problem (R2BP)
Solar system
Two body problem
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Summary:In this analytical study, a novel solving method for determining the precise coordinates of a mass point in orbit around a significantly more massive primary body, operating within the confines of the restricted two-body problem (R2BP), has been introduced. Such an approach entails the utilization of a continued fraction potential diverging from the conventional potential function used in Kepler’s formulation of the R2BP. Furthermore, a system of equations of motion has been successfully explored to identify an analytical means of representing the solution in polar coordinates. An analytical approach for obtaining the function t = t(r), incorporating an elliptic integral, is developed. Additionally, by establishing the inverse function r = r(t), further solutions can be extrapolated through quasi-periodic cycles. Consequently, the previously elusive restricted two-body problem (R2BP) with a continued fraction potential stands fully and analytically solved.
ISSN:2227-7390
2227-7390
DOI:10.3390/math12040590